(mathematics) A linear combination of positive and negative powers of a variable with coefficients in a given field. They differ from ordinary polynomials in that they may have terms of negative degree.

plural of Alexander polynomial

plural of Laurent polynomial

plural of Zhegalkin polynomial

(logic, algebra) A Boolean-valued polynomial formed as a XOR-sum (or "ring sum") of conjunctions.

(algebra) A linear combination of powers of an indeterminate (or products of powers of more than one indeterminate), with coefficients belonging to an integral domain or a field. (The indeterminate is thought of as an element extraneous to the set of coefficients, instead of as a variable element of it (as in the case of polynomial functions), just as, say, the square root of negative one is an element extraneous to the set of integers when it is adjoined to them to form the domain of Gaussian integers. The indeterminate forms a free commutative monoid, to which all powers of it belong, and the unity of it can also show up implicitly in the constant term of a polynomial form.)

(mathematics) A truncated Maclaurin series; the sum of the first n terms of a Maclaurin series.

(algebra) For a positive integer n, a polynomial whose roots are the primitive nᵗʰ roots of unity, so that its degree is Euler's totient function of n. That is, letting 𝜁ₙ=e^(i 2𝜋/n) be the first primitive nᵗʰ root of unity, then 𝛷ₙ(x)=∏_( stackrel )1<m<ngcd (n,m)=1(x-𝜁ₙᵐ) is the nᵗʰ such polynomial.

(mathematical analysis) A truncated Taylor series; the sum of the first n terms of a Taylor series.

plural of Taylor's polynomial